استقرار الاتزان الكهروهيدروديناميكى لموائع متعددة الطبقات تنساب على مستوى مائل

Electrohydrodynamic Stability of Multi-Layered Fluids Flowing Down an Inclined Plane  

                "The main aim of this thesis, which consists of three chapters and two appendices, is

to study two new problems of electrohydrodynamic instability of multi-layered

dilectric fluids flowing down an inclined plane and it can be summarized as follows:-

Chapter (1):-

The first chapter introduces a general introduction about the subject consists of the

following items:

1- The motion of fluids on inclined planes for two and three layers.

2- The basic equations of motion, in general, under the effects of streaming,

convection, and electric fields.

3- The appropriate boundary conditions for electrohydrodynamic stability

problems.

Chapter (2):-

In the second chapter we have studied the electrohydrodynamic instability of two

superposed dielectric fluids flowing down an inclined plane with upper rigid

boundary under the action of electric field normal to the interface, and with the

presence of thermal conductivity variation assuming that the density is varying

with temperature, and each of fluid viscosities and fluid depths are equal.

Applying perturbation technique to the basic equations of motion and boundary

conditions, we have obtained two Orr-Sommerfeld equations.

Using long-wave length approximation, we get the zero-order and first-order

solutions, and then we obtained the zero and first order values for wave velocity.

The effects all parameters such as thermal conductivity variation, Prandtl

number, Reynolds number, and dielectric constant ratio on the stability of the

system in absence and presence of electric field which has been found to have a

destabilizing influence.

Chapter (3):-

In the third chapter, we have studied the electrohydrodynamic instability of

multi-layered dielectric fluids flowing down an inclined plane with upper free

surface under the effect of tangential electric field to the interface.

Applying linear perturbation technique to the used equations of motion (Navier-

Stokes, Maxwell, and continuity equations), and the suitable boundary conditions,

we have obtained some Orr-Sommerfeld equations equal in number (n) to the

number of layers.

Using the previous approximation method too, we have obtained (3n) of linear

algebraic equations. We solve these equations assuming that n has two or three

layers only, became calculations are very difficult for n>3. Solving the equations

in both cases n=2, n=3 separately, we have obtained the wave velocity to the zero

and first order terms respectively in each case.

The effects of all parameters on the electrohydrodynamic instability of the

system by varying the electric field are discussed in detail, and we shown that the

electric field has a stabilizing effect, which all the other parameters have dual

roles on the stability depend on the corresponding electric field values.

Appendix (1):-

We introduced the constants of integration obtained in chapter (3) in the case of

n=2, i.e. when the fluid consists of two layers.

Appendix (2):-

We introduced the constants of integration obtained in chapter (3) in the case of

n=3, i.e. when the fluid consists of three layers."